Question

Your analysis of outcomes for sales and the associated rate of return on common stocks for companies X and Y are shown below. You intend to form a portfolio by allocating 30% of your funds in Company X, and the remainder in Company Y.

probability       ROR for X       ROR for Y      

declining                          25%                -1.0 %                6.3%   

flat                                   55                   10.7                  18.9   

rising                                20                   18.9                 -16.0

What is the expected return and standard deviation of portfolio returns?

The portfolio E(R) is 8.96% and the standard deviation is 8.87%

b. The portfolio E(R) is 8.96% and the standard deviation is 78.64%

c. The portfolio E(R) is 6.29% and the standard deviation is 6.68%

d. The portfolio E(R) is 5.98% and the standard deviation is 44.61%

e. The portfolio E(R) is 5.23% and the standard deviation is 3.86%

Answer 1

IF ANY QUERY, FEEL FREE TO ASK THEM AND GET RESOLVED Solution 1 Calculate portfolio's return at different state Portfolio State Probability Declining Flat 25.00% 55.00% 20.00% Stock X weight return 30.00% -1.00% 30.00% 10.70% 30.00% 18.90% Stock Y weight return 70.00% 6.30% 70.00% 18.90% 70.00% -16.00% Return 4.11% 16.44% -5.53% Rising 2 Expected portfolio return and Standard deviation calculation Deviation Deviation Portfolio State Probability Return Declining 25.00% 4.11% Flat 55.00% 16.44% Rising 20.00% -5.53% Expected Portfolio return (EPR) Return x Probability 1.0275% 9.0420% -1.1060% 8.96% -4.8535% 0.2356% 7.4765% 0.5590% -14.4935% 2.1006% Variance Standard Deviation DeviationⓇx Probability 0.0589% 0.3074% 0.4201% 0.7865% 8.87% where, Expected Portfolio return Deviation Sum of all (Probability x Portfolio return) Portfolio return - expected portfolio return Sum of all Deviation'x Probability 0.5 Variance Variance Standard Deviation Hence, option a. The portfolio E(R) is 8.96% and the standard deviation is 8.87% is correct.